{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Minimize beamwidth of an array with arbitrary 2-D geometry\n",
    "\n",
    "A derivative work by Judson Wilson, 5/14/2014.<br>\n",
    "Adapted (with significant changes) from the CVX example of the same name, by Almir Mutapcic, 2/2/2006.\n",
    "\n",
    "\n",
    "Topic References:\n",
    "\n",
    "* \"Convex optimization examples\" lecture notes (EE364) by S. Boyd\n",
    "* \"Antenna array pattern synthesis via convex optimization\" by H. Lebret and S. Boyd\n",
    "\n",
    "## Introduction\n",
    "\n",
    "This algorithm designs an antenna array such that:\n",
    "\n",
    "* it has unit sensitivity at some target direction  \n",
    "* it obeys a constraint on a minimum sidelobe level outside the beam\n",
    "* it minimizes the beamwidth of the pattern.\n",
    "\n",
    "This is a quasiconvex problem. Define the target direction as $\\theta_{\\mbox{tar}}$, and a beamwidth of $\\Delta \\theta_{\\mbox{bw}}$. The beam occupies the angular interval\n",
    "\n",
    "$$\\Theta_b = \\left(\\theta_{\\mbox{tar}}\n",
    "-\\frac{1}{2}\\Delta \\theta_{\\mbox{bw}},\\; \\theta_{\\mbox{tar}} \n",
    "+ \\frac{1}{2}\\Delta \\theta_{\\mbox{bw}}\\right).\n",
    "$$\n",
    "\n",
    "Solving for the minimum beamwidth $\\Delta \\theta_{\\mbox{bw}}$ is performed by bisection, where the interval which contains the optimal value is bisected  according to the result of the following feasibility problem:\n",
    "\n",
    "\\begin{array}{ll}\n",
    "\\mbox{minimize}   &  0 \\\\\n",
    "\\mbox{subject to} & y(\\theta_{\\mbox{tar}}) = 1 \\\\\n",
    "                  &  \\left|y(\\theta)\\right| \\leq t_{\\mbox{sb}} \n",
    "                         \\quad \\forall \\theta \\notin \\Theta_b.\n",
    "\\end{array}\n",
    "    \n",
    "$y$ is the antenna array gain pattern (a complex-valued function), $t_{\\mbox{sb}}$ is the maximum allowed sideband gain threshold, and the variables are $w$ (antenna array weights or shading coefficients). The gain pattern is a linear function of $w$: $y(\\theta) = w^T a(\\theta)$ for some $a(\\theta)$ describing the antenna array configuration and specs.\n",
    "\n",
    "Once the optimal beamwidth is found, the solution $w$ is refined with the following optimization:\n",
    "\n",
    "\\begin{array}{ll}\n",
    "\\mbox{minimize}   &  \\|w\\| \\\\\n",
    "\\mbox{subject to} & y(\\theta_{\\mbox{tar}}) = 1 \\\\\n",
    "                  & \\left|y(\\theta)\\right|  \\leq t_{\\mbox{sb}}\n",
    "                          \\quad \\forall \\theta \\notin \\Theta_b.\n",
    "\\end{array}\n",
    "\n",
    "The implementation below discretizes the angular quantities and their counterparts, such as $\\theta$.\n",
    "\n",
    "## Problem specification and data\n",
    "\n",
    "### Antenna array selection\n",
    "\n",
    "Choose either:\n",
    "\n",
    "* A random 2D positioning of antennas.\n",
    "* A uniform 1D positioning of antennas along a line.\n",
    "* A uniform 2D positioning of antennas along a grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cvxpy as cp\n",
    "import numpy as np\n",
    "\n",
    "# Select array geometry:\n",
    "ARRAY_GEOMETRY = '2D_RANDOM'\n",
    "#ARRAY_GEOMETRY = '1D_UNIFORM_LINE'\n",
    "#ARRAY_GEOMETRY = '2D_UNIFORM_LATTICE'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data generation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "# Problem specs.\n",
    "#\n",
    "lambda_wl = 1         # wavelength\n",
    "theta_tar = 0           # target direction\n",
    "min_sidelobe = -20    # maximum sidelobe level in dB\n",
    "\n",
    "max_half_beam = 50    # starting half beamwidth (must be feasible)\n",
    "\n",
    "#\n",
    "# 2D_RANDOM: \n",
    "#     n randomly located elements in 2D.\n",
    "#\n",
    "if ARRAY_GEOMETRY == '2D_RANDOM':\n",
    "    # Set random seed for repeatable experiments.\n",
    "    np.random.seed(1)\n",
    "    # Uniformly distributed on [0,L]-by-[0,L] square.\n",
    "    n = 36\n",
    "    L = 5\n",
    "    loc = L*np.random.random((n,2))\n",
    "\n",
    "#\n",
    "# 1D_UNIFORM_LINE:\n",
    "#     Uniform 1D array with n elements with inter-element spacing d.\n",
    "#\n",
    "elif ARRAY_GEOMETRY == '1D_UNIFORM_LINE':\n",
    "    n = 30\n",
    "    d = 0.45*lambda_wl\n",
    "    loc = np.hstack(( d * np.array(range(0,n)).reshape(-1, 1), \\\n",
    "                          np.zeros((n,1)) ))\n",
    "\n",
    "#\n",
    "# 2D_UNIFORM_LATTICE:\n",
    "#     Uniform 2D array with m-by-m element with d spacing.\n",
    "#\n",
    "elif ARRAY_GEOMETRY == '2D_UNIFORM_LATTICE':\n",
    "    m = 6\n",
    "    n = m**2\n",
    "    d = 0.45*lambda_wl\n",
    "\n",
    "    loc = np.zeros((n, 2))\n",
    "    for x in range(m):\n",
    "        for y in range(m):\n",
    "            loc[m*y+x,:] = [x,y]\n",
    "    loc = loc*d\n",
    "\n",
    "else:\n",
    "    raise Exception('Undefined array geometry')\n",
    "\n",
    "\n",
    "#\n",
    "# Construct optimization data.\n",
    "#\n",
    "\n",
    "# Build matrix A that relates w and y(theta), ie, y = A*w.\n",
    "theta = np.array(range(1, 360+1)).reshape(-1, 1)\n",
    "A = np.kron(np.cos(np.pi*theta/180), loc[:, 0].T) \\\n",
    "  + np.kron(np.sin(np.pi*theta/180), loc[:, 1].T)\n",
    "A = np.exp(2*np.pi*1j/lambda_wl*A)\n",
    "\n",
    "# Target constraint matrix.\n",
    "ind_closest = np.argmin(np.abs(theta - theta_tar))\n",
    "Atar = A[ind_closest,:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solve using bisection algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We are only considering integer values of the half beam-width\n",
      "(since we are sampling the angle with 1 degree resolution).\n",
      "\n",
      "Problem is feasible for half beam-width = 26.0 degress\n",
      "Problem is feasible for half beam-width = 14.0 degress\n",
      "Problem is not feasible for half beam-width = 8.0 degress\n",
      "Problem is feasible for half beam-width = 11.0 degress\n",
      "Problem is feasible for half beam-width = 10.0 degress\n",
      "Problem is not feasible for half beam-width = 9.0 degress\n",
      "Optimum half beam-width for given specs is 10.0\n",
      "final objective value: 1.33693666264\n"
     ]
    }
   ],
   "source": [
    "# Bisection range limits. Reduce by half each step.\n",
    "halfbeam_bot = 1\n",
    "halfbeam_top = max_half_beam\n",
    "\n",
    "print('We are only considering integer values of the half beam-width')\n",
    "print('(since we are sampling the angle with 1 degree resolution).')\n",
    "print('')\n",
    "\n",
    "# Iterate bisection until 1 angular degree of uncertainty.\n",
    "while halfbeam_top - halfbeam_bot > 1:\n",
    "    # Width in degrees of the current half-beam.\n",
    "    halfbeam_cur = np.ceil( (halfbeam_top + halfbeam_bot)/2.0 )\n",
    "\n",
    "    # Create optimization matrices for the stopband,\n",
    "    # i.e. only A values for the stopband angles.\n",
    "    upper_beam = (theta_tar + halfbeam_cur) % 360\n",
    "    lower_beam = (theta_tar - halfbeam_cur) % 360\n",
    "    if upper_beam > lower_beam:\n",
    "        ind = np.nonzero(np.squeeze(np.array(np.logical_or( \\\n",
    "                        theta <= lower_beam, \\\n",
    "                        theta >= upper_beam ))))\n",
    "    else:\n",
    "        ind = np.nonzero(np.squeeze(np.array(np.logical_and( \\\n",
    "                        theta <= lower_beam, \\\n",
    "                        theta >= upper_beam ))))\n",
    "    \n",
    "    As = A[ind[0],:]\n",
    "    \n",
    "    #\n",
    "    # Formulate and solve the feasibility antenna array problem.\n",
    "    #\n",
    "\n",
    "    # As of this writing (2014/05/14) cvxpy does not do complex valued math,\n",
    "    # so the real and complex values must be stored separately as reals\n",
    "    # and operated on as follows:\n",
    "    #     Let any vector or matrix be represented as a+bj, or A+Bj.\n",
    "    #     Vectors are stored [a; b] and matrices as [A -B; B A]:\n",
    "    \n",
    "    # Atar as [A -B; B A]\n",
    "    Atar_R = Atar.real\n",
    "    Atar_I = Atar.imag\n",
    "    neg_Atar_I = -Atar_I\n",
    "    Atar_RI = np.block([[Atar_R, neg_Atar_I], [Atar_I, Atar_R]])\n",
    "\n",
    "    # As as [A -B; B A]\n",
    "    As_R = As.real\n",
    "    As_I = As.imag\n",
    "    neg_As_I = -As_I\n",
    "    As_RI = np.block([[As_R, neg_As_I], [As_I, As_R]])\n",
    "    As_RI_top = np.block([As_R, neg_As_I])\n",
    "    As_RI_bot = np.block([As_I, As_R])\n",
    "\n",
    "    # 1-vector as [1, 0] since no imaginary part\n",
    "    realones_ri = np.array([1.0, 0.0])\n",
    "\n",
    "    # Create cvxpy variables and constraints\n",
    "    w_ri = cp.Variable(shape=(2*n))\n",
    "    constraints = [ Atar_RI*w_ri == realones_ri]\n",
    "    # Must add complex valued constraint \n",
    "    # abs(As*w <= 10**(min_sidelobe/20)) row by row by hand.\n",
    "    # TODO: Future version use norms() or complex math\n",
    "    # when these features become available in cvxpy.\n",
    "    for i in range(As.shape[0]):\n",
    "        #Make a matrix whos product with w_ri is a 2-vector\n",
    "        #which is the real and imag component of a row of As*w\n",
    "        As_ri_row = np.vstack((As_RI_top[i, :], As_RI_bot[i, :]))\n",
    "        constraints.append( \\\n",
    "                cp.norm(As_ri_row*w_ri) <= 10**(min_sidelobe/20) )\n",
    "\n",
    "    # Form and solve problem.\n",
    "    obj = cp.Minimize(0)\n",
    "    prob = cp.Problem(obj, constraints)\n",
    "    prob.solve(solver=cp.CVXOPT)\n",
    "\n",
    "    # Bisection (or fail).\n",
    "    if prob.status == cp.OPTIMAL:\n",
    "        print('Problem is feasible for half beam-width = {}'\n",
    "              ' degress'.format(halfbeam_cur))\n",
    "        halfbeam_top = halfbeam_cur\n",
    "    elif prob.status == cp.INFEASIBLE:\n",
    "        print('Problem is not feasible for half beam-width = {}'\n",
    "              ' degress'.format(halfbeam_cur))\n",
    "        halfbeam_bot = halfbeam_cur\n",
    "    else:\n",
    "        raise Exception('CVXPY Error')\n",
    "\n",
    "# Optimal beamwidth.\n",
    "halfbeam = halfbeam_top\n",
    "upper_beam = (theta_tar + halfbeam) % 360\n",
    "lower_beam = (theta_tar - halfbeam) % 360\n",
    "print('Optimum half beam-width for given specs is {}'.format(halfbeam))\n",
    "\n",
    "# Compute the minimum noise design for the optimal beamwidth\n",
    "if upper_beam > lower_beam:\n",
    "    ind = np.nonzero(np.squeeze(np.array(np.logical_or( \\\n",
    "                    theta <= lower_beam, \\\n",
    "                    theta >= upper_beam ))))\n",
    "else:\n",
    "    ind = np.nonzero(np.squeeze(np.array(np.logical_and( \\\n",
    "                    theta <= lower_beam, \\\n",
    "                    theta >= upper_beam ))))\n",
    "        \n",
    "As = A[ind[0],:]\n",
    "\n",
    "# As as [A -B; B A]\n",
    "# See earlier calculations for real/imaginary representation\n",
    "As_R = As.real\n",
    "As_I = As.imag\n",
    "neg_As_I = -As_I\n",
    "As_RI = np.block([[As_R, neg_As_I], [As_I, As_R]])\n",
    "As_RI_top = np.block([As_R, neg_As_I])\n",
    "As_RI_bot = np.block([As_I, As_R])\n",
    "\n",
    "constraints = [ Atar_RI*w_ri == realones_ri]\n",
    "# Same constraint as a above, on new As (hense different\n",
    "# actual number of constraints). See comments above.\n",
    "for i in range(As.shape[0]):\n",
    "    As_ri_row = np.vstack((As_RI_top[i, :], As_RI_bot[i, :]))\n",
    "    constraints.append( \\\n",
    "        cp.norm(As_ri_row*w_ri) <= 10**(min_sidelobe/20) )\n",
    "\n",
    "# Form and solve problem.\n",
    "# Note the new objective!\n",
    "obj = cp.Minimize(cp.norm(w_ri))\n",
    "prob = cp.Problem(obj, constraints)\n",
    "prob.solve(solver=cp.SCS)\n",
    "\n",
    "#if prob.status != cp.OPTIMAL:\n",
    "#    raise Exception('CVXPY Error')\n",
    "print(\"final objective value: {}\".format(obj.value))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Show plot inline in ipython.\n",
    "%matplotlib inline\n",
    "\n",
    "# Plot properties.\n",
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')\n",
    "\n",
    "#\n",
    "# First Figure: Antenna Locations\n",
    "#\n",
    "plt.figure(figsize=(6, 6))\n",
    "plt.scatter(loc[:, 0], loc[:, 1],\n",
    "            s=30, facecolors='none', edgecolors='b')\n",
    "plt.title('Antenna Locations', fontsize=16)\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "#\n",
    "# Second Plot: Array Pattern\n",
    "#\n",
    "\n",
    "# Complex valued math to calculate y = A*w_im;\n",
    "# See comments in code above regarding complex representation as reals.\n",
    "A_R = A.real\n",
    "A_I = A.imag\n",
    "neg_A_I = -A_I\n",
    "A_RI = np.block([[A_R, neg_A_I], [A_I, A_R]]);\n",
    "\n",
    "y = A_RI.dot(w_ri.value)\n",
    "y = y[0:int(y.shape[0]/2)] + 1j*y[int(y.shape[0]/2):] #now native complex\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "ymin, ymax = -40, 0\n",
    "plt.plot(np.arange(360)+1, np.array(20*np.log10(np.abs(y))))\n",
    "plt.plot([theta_tar, theta_tar], [ymin, ymax], 'g--')\n",
    "plt.plot([upper_beam, upper_beam], [ymin, ymax], 'r--')\n",
    "plt.plot([lower_beam, lower_beam], [ymin, ymax], 'r--')\n",
    "plt.xlabel('look angle', fontsize=16)\n",
    "plt.ylabel(r'mag $y(\\theta)$ in dB', fontsize=16)\n",
    "plt.ylim(ymin, ymax)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "#\n",
    "# Third Plot: Polar Pattern\n",
    "#\n",
    "plt.figure(figsize=(6,6))\n",
    "zerodB = 50\n",
    "dBY = 20*np.log10(np.abs(y)) + zerodB\n",
    "plt.plot(dBY * np.cos(np.pi*theta.flatten()/180),\n",
    "         dBY * np.sin(np.pi*theta.flatten()/180))\n",
    "plt.xlim(-zerodB, zerodB)\n",
    "plt.ylim(-zerodB, zerodB)\n",
    "plt.axis('off')\n",
    "\n",
    "# 0 dB level.\n",
    "plt.plot(zerodB*np.cos(np.pi*theta.flatten()/180),\n",
    "         zerodB*np.sin(np.pi*theta.flatten()/180), 'k:')\n",
    "plt.text(-zerodB,0,'0 dB', fontsize=16)\n",
    "# Max sideband level.\n",
    "m=min_sidelobe + zerodB\n",
    "plt.plot(m*np.cos(np.pi*theta.flatten()/180),\n",
    "         m*np.sin(np.pi*theta.flatten()/180), 'k:')\n",
    "plt.text(-m,0,'{:.1f} dB'.format(min_sidelobe), fontsize=16)\n",
    "#Lobe center and boundaries angles.\n",
    "theta_1 = theta_tar+halfbeam\n",
    "theta_2 = theta_tar-halfbeam\n",
    "plt.plot([0, 55*np.cos(theta_tar*np.pi/180)], \\\n",
    "         [0, 55*np.sin(theta_tar*np.pi/180)], 'k:')\n",
    "plt.plot([0, 55*np.cos(theta_1*np.pi/180)], \\\n",
    "         [0, 55*np.sin(theta_1*np.pi/180)], 'k:')\n",
    "plt.plot([0, 55*np.cos(theta_2*np.pi/180)], \\\n",
    "         [0, 55*np.sin(theta_2*np.pi/180)], 'k:')\n",
    "\n",
    "#Show plot.\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
